White matter in the brain is the wiring that enables functional networks and allows their intercommunication. Neural signals are processed in the cortex and transmitted to different regions of the brain through white matter pathways. White matter pathways can be categorized into commissural fibers, which connect regions between hemispheres; association fibers, which connect regions in the same hemisphere; and projection fibers, which establish connections between cortical and subcortical areas. Determination of those axonal pathways provides invaluable means to reveal the human brain's connectivity, which is fundamental to the study of brain function.
While the basic anatomy of white matter tracts in the human brain is known in general from anatomic dissection, much is unknown about the natural variation and association with age, sex, handedness and laterality, as well as abnormalities in many neuropsychiatric, neurologic and developmental disorders. In autism, for example, subtle, yet distinct, abnormalities in white matter have been observed, yet much remains to be characterized. White matter has traditionally been underemphasized relative to the gray matter in the study of many of those disorders. Recent advances in neuroimaging have enabled tremendous growth in the study of the human brain. While fMRI (functional magnetic resonance imaging) essentially enables the study of the gray matter, diffusion weighted magnetic resonance imaging (DW-MR) enables the study of white matter. DW-MR enables the in vivo measurement of the passive diffusion (random displacement) of water molecules. DW-MR is unique in its ability to capture the restricted diffusion of water molecules seen in fibrous tissues. Information derived from diffusion images can be used to infer the structural organization of such tissue components. In one technique of DW-MR, diffusion tensor imaging (DTI), each scan comprises at least six gradient directions, which are used to compute a diffusion tensor.
In human tissue, the mobility of water molecules is isotropic and its motion is limited by the presence of tissue components such as cell membranes and fibers. When those elements are aligned, the diffusion becomes directionally preferential and thus anisotropic. In the white matter, axons are organized in parallel bundles and water diffuses preferentially in the direction of the axonal fibers. The higher diffusion hindrance that is exhibited across the axonal axes is believed to be due to cell membranes and cytoskeletal structures. While the real source of the measured anisotropic diffusion (i.e., how much is due to extracellular spaces or due to intra-axonal microtubules and microfilaments) is not fully understood, it is clear that it directly reflects the underlying oriented axonal structure. Validation has been done, for example, using capillary tube phantoms and with contrast enhanced rat brain images.
The anisotropic diffusion that is observed in the white matter can be captured by diffusion-weighted images, and is represented by a signal decrease due to diffusive motion in the direction of the applied gradient field. The apparent diffusion which is measured by DW-MR does not simply depend on the viscosity but also on the cellular structure of the tissue. That degree of anisotropy reflects some combination of integrity, directional uniformity and density of the underlying fiber structure. The magnitude of the anisotropy and the dominant diffusion direction can be readily measured by DW-MR.
The Stejkal-Tanner equation governing the spin-echo intensity at each location x at angle (Θ, Φ) is:s(x, Θ, Φ)=s0e−bd(x,Θ,Φ)
where s0 is the non-diffusion weighted signal and d is the apparent diffusion at that angle. b is the diffusion-sensitizing gradient factor and is a function of the gyro magnetic ratio of the proton as well as the gradient strength and timings of the diffusion-sensitizing gradients. In diffusion tensor imaging (DTI), the local diffusion is modeled as an anisotropic Gaussian which can be described by a second order tensor. In that case, the above equation becomes:s(x, Θ, Φ)=s0e−bvTDv
where D is the apparent diffusion tensor and v is the diffusion direction. By acquiring diffusion-weighted data in at least six non-collinear directions, it is possible to estimate this 3×3 symmetric diffusion tensor. Diagonalization of the tensor matrix yields its eigenvalues and eigenvectors, which represent the main diffusion orientations. The eigenvector corresponding to the largest eigenvalue of the tensor is the main direction of diffusion and is taken as parallel to the local tangent of a fiber bundle.
Advances in DW-MR have now made possible quantitative analysis of white matter in the brain. Progress in understanding the macroscopic neuropathology of white matter disorders will be greatly enhanced by reliable, valid and efficient means of white matter quantification. The present invention includes techniques and an automated computer system for the analysis of brain white matter from DW-MR imaging data. The techniques will be applicable to many white matter disorders, and will provide an accurate and efficient comprehensive framework for the study of white matter structure crucial to the understanding of the brain and patients with disorders of white matter.
More specifically, the inventor proposes a novel method believed to yield better results especially when the measured data has a low signal-to-noise ratio (SNR). One of the problems faced by researchers in fiber tractography is that the diffusion-weighted images from which the DTI is inferred are particularly noise sensitive in view of the high degree of signal attenuation needed for suitable diffusion weighting. The widely used method to compute the tensor data from the raw diffusion-weighted images is particularly error-prone simply because it doesn't take into consideration any noise removal strategies. That can lead to errors in the major eigenvector direction and artificially increase the anisotropy. Those factors can lead to spurious connection when none exists originally, due to track drifting.
Often the deviation from a high SNR happens in practice because the image quality is compromised for feasible imaging times. A larger voxel size improves the SNR but leads to partial volume effects. If multiple fibers pass through a single voxel, that could result in an isotropic reading that completely belies the underlying realty.
There has been some effort to resolve those problems by doing diffusion spectrum imaging. For example, in J. D. Tournier et al., Diffusion weighted magnetic resonance fiber tracking using a front evolution algorithm, 20 NeuroImage 276-288 (2003), the authors take a representative sample of the most likely directions at each point, and each sample is allocated its index of connectivity. In other words, several paths are evaluated at every point before settling on the dominant one. That solution takes into account some measure of neighborhood inference. In C. Chefd'hotel, D. Tschumperl, R. Deriche, and O. Faugeras, Constrained flow of matrix valued functions: Application to diffusion tensor regularization, Proceedings of the ECCV 251-265 (2000), the tensor field is regularized and is constrained to be positive definite.
Advances in diffusion weighted magnetic resonance (DW-MR) imaging have made possible the detailed quantitative analysis of white matter in the brain. Diffusion imaging has been most successful in the study of large white matter tracts, such as the corpus callosum and corticospinal tracts, which consist of tightly packed fiber bundles coursing in the same direction. Other tracts, however, are intermingled with fibers that course in various directions. As a result, their depiction has often been imprecise, as it is based on sketches of the tracts, not on precise data provided by dissected material. Progress in understanding the macroscopic neuropathology of white matter disorders would be greatly enhanced by reliable, valid and efficient means of white matter quantification.
However, reliable tracking and quantification is impossible unless the acquired image quality can be improved. There is therefore presently a need for a method and system for reducing noise in a diffusion tensor image, thereby improving the image quality without losing important information regarding fiber crossings. To the inventor's knowledge, no such techniques are currently available.